Question

(a) A voltaic cell is constructed with all reactants and products in their standard states. Will this condition hold as the cell operates? Explain. (b) Can the Nernst equation be used at temperatures other than room temperature? Explain. (c) What happens to the emf of a cell if the concentrations of the products are increased?

Short answer

(a) No, the standard state condition will not hold as the cell operates. As reactants are consumed and products are generated, concentrations change, and the cell potential will decrease as the reaction progresses toward equilibrium. (b) Yes, the Nernst equation can be used at temperatures other than room temperature. Since the temperature appears explicitly in the equation, it can be used to calculate the cell potential at any given temperature by substituting the appropriate value for T. (c) As the product concentrations increase, the emf of a cell will decrease. This is because an increase in product concentrations leads to an increase in the reaction quotient Q, causing a decrease in cell potential (E) according to the Nernst equation.

Step-by-step solution

(a) Explanation of standard state condition in a voltaic cell

A standard state is defined as a situation where the concentration of each reactant and product is at 1 M, the pressure of gases is at 1 atm, and the temperature is 25°C (298 K). However, as the voltaic cell operates, the concentrations of reactants and products will change. Specifically, reactants will be consumed and products will be generated. Hence, the standard state condition will not hold as the cell operates. The cell potential will ultimately decrease as the reaction progresses toward equilibrium.

(b) Nernst equation and its applicability at different temperatures

The Nernst equation is a mathematical relationship that can be used to determine the cell potential at non-standard conditions. It is given by: \(E = E° - \frac{RT}{nF} \ln Q\) Where E is the cell potential, E° is the standard cell potential, R is the gas constant, T is the temperature in Kelvin, n is the number of electrons transferred in the redox reaction, F is the Faraday's constant, and Q is the reaction quotient. The Nernst equation can be used at temperatures other than room temperature (298 K). Since the temperature appears explicitly in the equation, it can be used to calculate the cell potential at any given temperature by substituting the appropriate value for T.

(c) Effect of product concentration on the emf of a cell

As the product concentrations increase, the reaction quotient (Q) in the Nernst equation will also increase. According to the Nernst equation: \(E = E° - \frac{RT}{nF} \ln Q\) An increase in Q will lead to an increase in the natural logarithm term (\(\ln Q\)), which in turn will increase the entire term\(\frac{RT}{nF} \ln Q\). Since this term is subtracted from the standard cell potential (E°), an increase in the product concentrations will result in a decrease in the cell potential (E). Therefore, the emf of a cell will decrease when the concentrations of the products are increased.